In
constructive (and classical) logic the negation \(\lnot A\)  of a formula \(A\)  can be defined in a negative way as
the implication \(A \rightarrow \bot \) , where \(\bot \)  denotes “falsum”. Constructively though, \(\lnot A\)  has a weak behaviour,
as the negation of a conjunction
\(\lnot (A \wedge B)\)  does not generally imply the disjunction \(\lnot A \vee \lnot B\) , and similarly the negation of
a universal
formula \(\lnot \forall _x A(x)\)  does not generally imply the existential formula \(\exists _x \lnot A(x)\) .
Even if \(A\)  and \(B\)  are stable i.e., \(\lnot \lnot A \rightarrow A\)  and \(\lnot \lnot B \rightarrow B\) , we only get
\(\lnot (A \wedge B) \vdash \lnot \lnot (\lnot A \vee \lnot B)\)  and \(\lnot \forall _x A(x)\vdash \lnot \lnot \exists _x \lnot A(x)\) , where \(\vdash \)  is the derivability relation in minimal logic.
For this reason, \(\lnot A\)  is called the weak negation of \(A\) , which, according to Rasiowa [1]}, p. 276
is not constructive, exactly due to its aforementioned behaviour.
